System and method for calibrating fuel injectors in an engine control system that calculates injection duration by mathematical formula

ABSTRACT

A method of modifying a general formula that is used by an engine control system ( 10 ) to calculate duration of fuel injector actuation. Coefficients (P1 coeff., P2 coeff., ICP coeff.) of the formula are modified to calibrate individual fuel injectors ( 16 ) in an engine. The amount of calibration needed is determined by data that is marked on each fuel injector in electronically readable format after the fuel injector has been operated and its operating characteristic ascertained. The control system reads the marked data and then makes the proper coefficient adjustment.

FIELD OF THE INVENTION

[0001] This invention relates generally to internal combustion engineshaving electric-actuated fuel injectors that inject fuel into combustionchambers of the engine. More particularly it relates to a system andmethod that uses several variables, including injector control pressureand the duration of an injector-actuation signal applied to the fuelinjectors, in a process that calculates, by a mathematical formula, thequantity of fuel injected by a fuel injector during an injection, andthat calibrates each fuel injector by adjustment of the formula.

BACKGROUND OF THE INVENTION

[0002] A known electronic engine control system comprises aprocessor-based engine controller that processes various data to developfueling data for the engine. The fueling data represents a quantity offuel that is to be introduced into the engine for combustion. Thatcontrol system also includes an injector control module, or injectordriver module, for operating fuel injectors that inject fuel into theengine in quantities corresponding to the fueling data. The fueling datais supplied to the injector control module from the engine controller,and the injector control module has its own processor for processing thesupplied data to develop proper data for causing the fuel injectors toinject fuel in quantities corresponding to the fueling data calculatedby the engine controller. For any one or more of various reasons thatneed not be discussed here, the injector control module may also makecertain adjustments to the supplied data when the engine controlstrategy and/or injector calibration make it appropriate to do so.

[0003] The injector control module also comprises injector drivers eachof which delivers an electric current signal to an electric actuator ofthe respective fuel injector. A fuel injector may have one or moreelectric actuators depending on its particular construction. The signalthat is applied to a fuel injector to cause an injection of fuel iscommonly referred to generically as a pulse width modulated signal. Inthe case of a fuel injector that has a single actuator, the actuatingsignal is a true pulse whose width sets the amount of time of aninjection, and hence essentially determines the quantity of fuel thatthe fuel injector injects into the corresponding engine cylinder inconsequence of that applied pulse. In the known engine controller thatis being referred to, it is the injector control module that calculatesthe pulse width by processing the fueling data supplied to it by theengine controller.

[0004] The particular nature of the electric actuation of any particularfuel injector depends on the particular construction of the fuelinjector. There is the single actuator type mentioned above. Anothertype of fuel injector, one for a compression-ignition internalcombustion engine, comprises an intensifier piston for creating ahigh-pressure injection of fuel directly into an associated enginecylinder. The intensifier piston comprises a head of given end areaexposed to a control fluid, oil for example, in a control chamber, and aplunger, or rod, of smaller end area exposed to liquid fuel in aninjection chamber. The electric actuator comprises a spool valve thatuses two electric actuators, i.e. solenoid coils, to control theintroduction of pressurized control fluid into the control chamber andthe draining of control fluid from the control chamber.

[0005] When an electric signal for initiating a fuel injection isapplied to one of the two electric actuators for the spool valve,control fluid is introduced under pressure through one portion of thespool valve into the control chamber to downstroke the intensifierpiston and cause fuel in the injection chamber to be injected underpressure from a nozzle of the fuel injector into an associated enginecylinder. The intensifier piston amplifies the pressure of the controlfluid by a factor equal to the ratio of the head end area to the plungerend area to cause the amplified pressure to be applied to liquid fuel inthe injection chamber. As a result, fuel is injected into a combustionchamber at a pressure substantially greater than the pressure of thecontrol fluid.

[0006] When an electric signal for terminating the fuel injection isapplied to the other electric actuator, the spool valve operates toterminate the downstroke of the intensifier piston and instead allowcontrol fluid to drain from the control chamber through another portionof the spool valve so that the intensifier piston can then upstroke tore-charge the injection chamber with liquid fuel in preparation for thenext injection.

[0007] Examples of fuel injectors having valves like those justdescribed appear in U.S. Pat. Nos. 3,837,324; 5,460,329; 5,479,901; and5,597,118.

[0008] Where a single electric actuator controls a fuel injector valve,the beginning of an electric pulse applied to the actuator initiates aninjection, and the injection terminates when the pulse ends. Theinjection time is therefore set by the width, i.e. time duration, of theactual electric pulse applied to the injector actuator.

[0009] Commonly assigned U.S. Pat. No. 6,029,628 is an example of a fuelinjector comprising two electric actuators that operate respective valvemechanisms. A supply valve mechanism is controlled by an electric supplyvalve actuator for selectively controlling flow of control fluid througha supply passage for downstroking an intensifier piston. A drain valvemechanism is controlled by an electric drain valve actuator forselectively controlling flow of control fluid through a drain passage.Each valve actuator is selectively operable independent of the other toselectively operate the respective valve mechanism independent of theother. Actuation of the supply valve mechanism while the drain valvemechanism is not being actuated initiates an injection, and theinjection terminates when the drain valve mechanism is actuated.

[0010] The use of two electric signals, each applied to a respective oneof the two actuators, to set the duration of a fuel injection is likethat described previously for the fuel injector that has two actuatorsfor operating a spool valve because the difference between the times atwhich the two actuators are actuated, rather than the time duration ofan actual electric pulse, controls the duration of an injection. But thetwo signals in effect define a pulse width for operating the fuelinjector that is equivalent to the pulse width of a single pulse signalthat determines the injection time of a fuel injector that has only asingle electric actuator. Hence, reference to pulse width in a genericcontext should be understood to include an actual pulse width of asingle signal or an equivalent pulse width resulting from the use of onesignal to initiate an injection and another signal to terminate theinjection.

[0011] The known engine controller also contains one or more look-uptables that its processor uses to calculate the desired fueling data,which is then processed to calculate the widths of electric pulses thatoperate the fuel injectors. The look-up tables are derived from actualtesting of fuel injectors. Fuel injectors are mapped for variouscombinations of values for injector control pressure and actuatingsignal pulse width. Each combination of values defines a correspondingvalue for desired fueling data. A sufficient number of combinations areneeded to cover the relevant ranges of the variables, but the availablesize of the look-up tables ultimately determines how many combinationscan actually be stored in memory of the controller.

[0012] While increasing look-up table size, and hence the number ofcombinations that can be stored, will endow the tables with a higherdegree of resolution that may be desirable for increased fuelingaccuracy, the increased size of the electronic storage medium that isrequired to contain the stored data increases the cost of thecontroller. A greater amount of mapping is also required in order toobtain the greater amount of data.

[0013] A lesser number of stored combinations may decrease theresolution, and hence decrease fueling accuracy. The processor may thenon occasion have to interpolate the mapped data in order to yielddesired fueling data, and where non-linearity is present in the fuelinjector, linear interpolation may not yield the accuracy that would beobtained from a larger table of greater resolution.

[0014] Regardless of fuel injector type or of how fuel injector data ismapped into a controller, fuel injector calibration is also importantfor securing desired fueling. Mass production methods inherently resultin some variation in calibration from fuel injector to fuel injector,and while such methods may strive to minimize the range of thesevariations, the ranges remain significant enough that someclassification of fuel injectors according to a number of differentcalibration categories, or groups, is appropriate in a mass productionenvironment. The mapping of fuel injector data that has been describedabove may therefore represent mean data obtained from mapping a numberof individual fuel injectors statistically representative of a universeof fuel injectors, in which case the calculated fueling data may befurther processed to account for individual fuel injector calibration.

[0015] Hence, before it is assembled to an engine, a mass-produced fuelinjector is operated to ascertain its actual calibration. The actualcalibration determines into which particular one of a number ofdifferent calibration categories the fuel injector falls. The fuelinjector is then identified by that particular category. When an engineis being manufactured, the associated engine controller is programmed insuch a way that the particular calibration category of the fuel injectorfor each particular engine cylinder is made available to the controller.The controller uses that data to calibrate electric control signals tothe fuel injectors, typically to secure injection of fuel insubstantially equal quantities to each combustion chamber for a givenvalue of fueling data calculated by the engine controller.

[0016] U.S. Pat. No. 5,575,264 discloses a method for associating actualperformance data with a fuel injector. The data is contained in amedium, such as an EEPROM, that is mounted on the fuel injector body andthat is suitable for reading by an associated engine controller.

[0017] U.S. Pat. No. 5,839,420 relates to a method for compensating afuel injection system for fuel injector variability. Each fuel injectorincludes a storage medium that contains a calibration code identifyingthe actual calibration of the fuel injector. An associated enginecontroller converts a raw energizing time to a calibrated energizingtime for each fuel injector based the calibration code for the fuelinjector.

[0018] U.S. Pat. No. 5,634,448 relates to another method for trimmingfuel injectors to compensate for fuel injector variability.

[0019] U.S. Pat. No. 4,402,294 relates to a system for calibrating fuelinjectors.

[0020] Other patents that relate to systems and methods for calculatingengine fueling and/or correcting the calculation for factors such asindividual fuel injector calibration are U.S. Pat. No. 4,379,332; U.S.Pat. No. 4,619,234; and U.S. Pat. No. 5,806,497.

[0021] Given the significant effort that is needed to map and calibratefuel injectors, and the amount of media needed to store a sufficientamount of mapped data to cover relevant ranges of variable parametersaffecting engine fueling, as discussed above, it would be desirable toprovide a system and a method that reduce the extent of the mappingeffort and of the amount of data storage that is needed. The inventor'scommonly assigned patent application “SYSTEM AND METHOD FOR PREDICTINGQUANTITY OF INJECTED FUEL AND ADAPTATION TO ENGINE CONTROL SYSTEM”, Ser.No. ______, filed of even date. (Attorney Docket No. D5122) relates tosuch a system and method.

SUMMARY OF THE INVENTION

[0022] The present invention is a further invention resulting from theinvention of Ser. No. ______ (Attorney Docket No. D5122), and concernscalibration of fuel injectors in an engine control system thatcalculates injection duration by mathematical formula.

[0023] Accordingly, a generic aspect of the present invention relates toa method of calibrating an electric-actuated fuel injector for an enginethat uses injector control pressure to inject the fuel from the injectorinto the engine. Before the fuel injector is installed in the engine, itis electrically actuated by a predetermined electric actuation at afirst predetermined injector control pressure. The resulting quantity offuel injected is measured. It is again electrically actuated by thepredetermined electric actuation but now at a second predeterminedinjector control pressure. The resulting quantity of fuel injected ismeasured. The measured quantities, the predetermined injection controlpressures, and the applied predetermined electric actuation arecorrelated with values of quantity of fuel injected, injector controlpressure, and electric actuation that are related by a predeterminedmultiple term mathematical formula to ascertain, for the same quantitiesof injected fuel at each predetermined injector control pressure,difference between the applied predetermined electric actuation and thatrequired by the formula.

[0024] Another generic aspect of the present invention relates to asystem that comprises apparatus for performing the method justdescribed.

[0025] Still another generic aspect of the present invention relates toan internal combustion engine comprising one or more electric-actuatedfuel injectors each of which injects fuel into a respective combustionchamber of the engine as a function of injector control pressure and theduration of an electric actuating signal that sets the duration of afuel injection to achieve an injection quantity determined at least inpart by a desired fueling data representing desired fueling of theengine. An engine control system comprises one or more processors thatcalculate the desired fueling data, and from the desired fueling data,the duration of the electric actuating signal for each fuel injector byprocessing the desired fueling data and data representing injectorcontrol pressure, including processing, according to a mathematicalformula, data correlated with the desired fueling data and datarepresenting injector control pressure, to develop data that the controlsystem further processes to calculate the duration of the electricactuating signal. Each fuel injector is marked with data that is enteredinto the engine control system incidental to installation of the fuelinjector in the engine and that defines difference between the operatingcharacteristic of the fuel injector and that of a general fuel injectoron which the multiple term mathematical formula is based. The controlsystem modifies the formula for each fuel injector according to themarked data on each fuel injector to thereby calibrate each fuelinjector in the engine so that each fuel injector injects fuelsubstantially in accordance with desired fueling data that is calculatedby the control system and then is used in the formula as the quantity ofinjected fuel.

[0026] The foregoing, along with further features and advantages of theinvention, will be seen in the following disclosure of a presentlypreferred embodiment of the invention depicting the best modecontemplated at this time for carrying out the invention. Thisspecification includes drawings, now briefly described as follows.

BRIEF DESCRIPTION OF THE DRAWINGS

[0027]FIG. 1 is a general schematic diagram of an exemplary embodimentof certain apparatus used in measuring the actual calibration of a fuelinjector.

[0028]FIG. 1A is a general schematic diagram of an exemplary engine andcontrol system embodying principles of the present invention.

[0029]FIG. 2 is a graph showing an example that illustrates certainsteps involved developing a general formula for calculating quantity offuel injected by a fuel injector.

[0030]FIG. 3 is a graph showing additional steps.

[0031]FIG. 3A shows a portion of FIG. 3 on a larger scale.

[0032]FIG. 4 is a graph showing correlation of actual fuelingmeasurements with calculated desired fueling derived through use of theinventive principles.

[0033]FIG. 5 is a graph showing the relationship between desired fuelingand pulse width for several different injector control pressures.

[0034]FIG. 6 is a graph similar to FIGS. 2 and 4, but with axesreversed, showing correlation of actual fueling measurements withcalculated desired fueling derived through further refinement of thegeneral equation.

[0035] FIGS. 7-11 are graphs of operating characteristics of severalfuel injectors useful in explaining principles of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0036]FIG. 1A shows a schematic diagram of an exemplary engine controlsystem 10 that utilizes results from a method that will subsequently bedescribed with reference to FIG. 1. Control system 10 comprises aprocessor-based engine controller 12 and an injector control module, orinjector driver module, 14 for controlling the operation ofelectric-actuated fuel injectors 16 that inject fuel into combustionchambers of an internal combustion engine 18, such as in amulti-cylinder, compression-ignition internal combustion engine thatpowers an automotive vehicle. Although FIG. 1A shows an arrangement foronly one cylinder 20, a respective fuel injector 16 is associated witheach cylinder. Each fuel injector comprises a body that is mounted onthe engine and has a nozzle through which fuel is injected into thecorresponding engine cylinder.

[0037] Controller 12 operates each fuel injector 16 via injector controlmodule 14, causing a respective driver circuit (not shown) in module 14to actuate the respective fuel injector at the appropriate time in theengine operating cycle. The processor of controller 12 processes variousitems of data to develop data representing desired quantities of fuel tobe injected by the individual fuel injectors. Such data will be referredto as desired fueling data represented by the symbol vfdes. The desiredfueling data is supplied to injector control module 14, which may haveits own processor for perform further processing of the supplied data todevelop data that is in turn converted to corresponding electric signalsfor the injector drivers that operate the fuel injectors. Datarepresenting the present injector control pressure ICP is also availableto injector control module 14.

[0038] Each fuel injector 16 comprises an electric-actuated injectionmechanism, such as one of the types described earlier. A fuel injectionfrom an injector is initiated by an initiating electric signal appliedto the fuel injector by the respective driver circuit. The fuelinjection terminates when the electric signal changes to a terminatingelectric signal. The initiating electric signal may be the leading edgeof a rectangular pulse, and the terminating signal, the trailing edge inthe case of an injector that has a single electric actuator. The timebetween the edges is the pulse width, which may be modulated accordingto the amount of fuel to be injected. Therefore, when a true pulse widthmodulated signal is used to operate the fuel injector, using the leadingedge of a pulse as an injection-initiating signal and the trailing edgeas an injection-terminating signal, the timing of the initiating andterminating electric signals determines the quantity of fuel injected,and the actual pulse width may be adjusted to take into account otherdata that at certain times is appropriate to use in making someadjustment of vfdes.

[0039] Injector control module 14 may therefore at times make certainadjustments to the desired fueling data vfdes received from controller12 for developing the pulse widths of the electric current signalssupplied to the fuel injectors. One reason for injector control module14 to make an adjustment of the desired fueling data that is suppliedfrom controller 12 is to compensate for certain characteristics of thespecific fuel injectors, such as the injector calibration mentionedabove, and that is the subject of the present invention. Another reasonfor adjustment of the desired fueling data, a reason that need not bediscussed here, is to compensate for prevailing conditions thatotherwise would contribute to deviation of the actual amount of fuelinjected from the desired amount, such as a cold start for example.

[0040] The desired fueling data vfdes supplied to injector controlmodule 14 represents a certain pulse width for the signal to be appliedto a fuel injector to deliver a corresponding amount of fuel to theengine cylinder based on some set of base conditions for the engine andambient.

[0041] In the case of a fuel injector that has two electric actuators,one of which is energized to initiate a fuel injection and the other ofwhich is energized to terminate the fuel injection, a respective signalis applied to each actuator. However, as explained above, the differencein time between the applications of the two signals is equivalent to apulse width of a single electric actuating signal. Further descriptionof the invention with reference to the drawing Figures is premised onthe fuel injectors being of the two-actuator type.

[0042] The invention of Ser. No. ______ (Attorney Docket No. D5122)relates to a system and method of deriving a formula for calculating aquantity of fuel injected by each such fuel injector 16. The methodcomprises mapping a representative fuel injector 16 by applying variouscombinations of different selected hydraulic fluid pressures anddifferent selected durations of the electric actuating signal. For eachcombination, the quantity of fuel injected is measured to create acorresponding data set for the combination. Each data set comprises thecorresponding selected hydraulic fluid pressure, the correspondingselected electric signal duration, and the quantity of fuel injected inconsequence of the application of the corresponding selected hydraulicfluid pressure and the corresponding selected electric signal durationto the fuel injector. The mapping apparatus is shown generally in FIG. 1and includes various pieces of measuring equipment and processingapparatus.

[0043] Because the fuel injector of the example has two electricactuators, a first signal P1 is used to initiate a fuel injection byenergizing one of the two actuators, and a second signal P2 is used toterminate the fuel injection by energizing the other of the twoactuators. Hence, the result of the mapping comprises a number of datasets each containing P1 data, P2 data, injector control pressure data,and injected fuel quantity data. The data sets are then sorted intogroups such that the injector control pressure data for the data sets ofa given group is the same. A multiple linear regression is conducted onthe data in each group. The following is an example of an actual mappingundertaken on a particular fuel injector. (A multiple polynomialregression can be undertaken injector control pressures that occurwithin a pressure range, low injector control pressures for example,where linearity is questionable.)

[0044] The equations used for the multiple linear regression are givenbelow as taken from Probability and Statistics for Engineers andScientists, Walpole and Myers. (2^(nd) edition 1978, 3^(rd) edition1985, MacMillan, NY, N.Y.).${{n\quad b_{o}} + {b_{1}{\sum\limits_{i = 1}^{n}x_{1i}}} + {b_{2}{\sum\limits_{i = 1}^{n}x_{2i}}} + {b_{3}{\sum\limits_{i = 1}^{n}x_{3i}}}} = {\sum\limits_{i = 1}^{n}y_{i}}$${{b_{o}{\sum\limits_{i = 1}^{n}x_{1i}}} + {b_{1}{\sum\limits_{i = 1}^{n}x_{1i}^{2}}} + {b_{2}{\sum\limits_{i = 1}^{n}{x_{1i}x_{2i}}}} + {b_{3}{\sum\limits_{i = 1}^{n}{x_{1i}x_{3i}}}}} = {\sum\limits_{i = 1}^{n}{x_{1i}y_{i}}}$${{b_{o}{\sum\limits_{i = 1}^{n}x_{2i}}} + {b_{1}{\sum\limits_{i = 1}^{n}{x_{1i}x_{2i}}}} + {b_{2}{\sum\limits_{i = 1}^{n}x_{2i}^{2}}} + {b_{3}{\sum\limits_{i = 1}^{n}{x_{2i}x_{3i}}}}} = {\sum\limits_{i = 1}^{n}{x_{2i}y_{i}}}$${{b_{o}{\sum\limits_{i = 1}^{n}x_{3i}}} + {b_{1}{\sum\limits_{i = 1}^{n}{x_{1i}x_{3i}}}} + {b_{2}{\sum\limits_{i = 1}^{n}{x_{2i}x_{3i}}}} + {b_{3}{\sum\limits_{i = 1}^{n}x_{3i}^{2}}}} = {\sum\limits_{i = 1}^{n}{x_{3i}y_{i}}}$

[0045] where x1=P1, x2=P2, x3=injector control pressure, n=the number ofmeasurements, and y=injected fuel quantity.

[0046] The equations are then solved for b₀, b₁, b₂, and b₃ at threedifferent injector control pressures, those pressure being 6 Mpa, 12Mpa, and 24 Mpa in the example. This resulted in the following equationsfor injected fuel quantity (fuel volume per injection, or stroke):${{@6}{Mp}\quad {a:{F\quad u\quad e\quad {l\left( \frac{{mm}^{3}}{S\quad t\quad r\quad o\quad k\quad e} \right)}}}} = {{{- 27.622} + {0.018*P_{1}} + {0.036*P_{2}} - {{0.029394@12}{Mp}\quad {a:{F\quad u\quad e\quad {l\left( \frac{{mm}^{3}}{S\quad t\quad r\quad o\quad k\quad e} \right)}}}}} = {{{- 32.51} + {0.021*P_{1}} + {0.057*P_{2}} - {{1.8775@24}{Mp}\quad {a:{F\quad u\quad e\quad {l\left( \frac{{mm}^{3}}{S\quad t\quad r\quad o\quad k\quad e} \right)}}}}} = {{- 18.391} + {0.025*P_{1}} + {0.082*P_{2}} - 8.8671}}}$

[0047] Plotting the actual data for each of the three injector controlpressures vs. their respective predicted values gives the correlationagreement shown in FIG. 2. As can be seen from the substantial 45 degreeline fit, the correlations on an individual basis are quite good,approximately 95%-96% confidence.

[0048] Because it is considered impractical to implement an infinitenumber of equations each of which would represent one of an infinitenumber of possible injected fuel quantities, the next step in theexample involves determining the equations which best represent theindividual coefficients. This can be done by plotting the coefficientsvs. injector control pressure for best fit as shown in FIGS. 3 and 3A.

[0049] From the equations for the line fits of the coefficients vs.injector control pressure, the following equations for the coefficientswere obtained:

Cons tan t=5.9847*ICP−40.211*{square root}{square root over(ICP)}+34.967

P1Coeff.=0.0029*{square root}{square root over (ICP)}+0.011

P2Coeff.=0.0187*{square root}{square root over (ICP)}−0.009

ICPCoeff.=−0.6625*ICP+3.3953*{square root}{square root over(ICP)}−4.3539

[0050] And then by applying the coefficients to terms of an equation andincluding a shift factor, the following generalized equation forinjected fuel quantity was developed:${{FuelDelivery}\left( \frac{{mm}^{3}}{S\quad t\quad r\quad o\quad k\quad e} \right)} = {13 + \left( {{5.9847*I\quad C\quad P} - {40.211*\sqrt{I\quad C\quad P}} + 34.967 + {\left( {{0.0029*\sqrt{I\quad C\quad P}} + 0.011} \right)*P_{1}} + {\left( {{0.0187*\sqrt{I\quad C\quad P}} - 0.009} \right)*P_{2}} + {\left( {{{- 0.6625}*I\quad C\quad P} + {3.3953*\sqrt{I\quad C\quad P}} - 4.3539} \right)*\sqrt{I\quad C\quad P}}} \right.}$

[0051] Hence, the foregoing shows that data from the data sets wasprocessed to create terms of a multiple term mathematical formula thatcan be used to calculate the quantity of fuel injected, wherein theterms of the formula include as variables, the electric signal durationand the hydraulic fluid pressure.

[0052]FIG. 4 verifies that the method of using the general equation, orformula, derived according to the inventive method, can calculate, withsatisfactory accuracy, injected fuel quantity based on P1, P2, andinjector control pressure for this type of injector within specifiedoperating ranges.

[0053] It is to be understood that each particular type of fuel injectormay require development of its own unique general equation, but fuelinjectors of the same type can be calibrated to an engine control systemin accordance with principles of the present invention.

[0054] The correlation shown by FIG. 5 is based on the linear segmentfor pressures between 6 and 24 Mpa in the particular example. Accuracybelow 6 Mpa and at maximum fuel deliveries is problematic due toinjector control pressure fluctuations as well as factors that createnon-linear conditions, and for such reasons, a multivariable polynomialregression may be required, as noted earlier.

[0055] Using the statistical software known as SIGMA PLOT, it ispossible to improve upon the general equation by using the non-linearregression model. Use of non-linear regression is premised upon havingderived the general equation, as described above. The general equationis entered into the SIGMA PLOT software as well as data sets for thethree independent variables (P1, P2, and injector control pressure) andthe one dependent variable (injected fuel quantity), and the curve fitwas tightened. The improved correlation agreement is shown in FIG. 6. AnR² value of 98% was found.

[0056] The refined equation is given as:${{FuelDelivery}\left( \frac{{mm}^{3}}{S\quad t\quad r\quad o\quad k\quad e} \right)} = {13 + \left( {{7.217*I\quad C\quad P} - {47.78*\sqrt{I\quad C\quad P}} + 34.967} \right) + {\left( {{0.008461*\sqrt{I\quad C\quad P}} + 0.011} \right)*P_{1}} + {\left( {{0.01866*\sqrt{I\quad C\quad P}} - 0.009} \right)*P_{2}} + {\left( {{{- 0.9927}*I\quad C\quad P} + {4.628*\sqrt{I\quad C\quad P}} - 4.3539} \right)*\sqrt{I\quad C\quad P}}}$

[0057] The development of a single empirical equation that can predictfuel deliveries over a range of 6-24 Mpa with a correlation agreement of98% is believed to afford opportunities to engine control strategydesigners and engine calibrators to significantly simplify controlstrategy and calibration procedures.

[0058] Processors of engine control systems can process datasufficiently fast to calculate, in real time, the duration of injectoractuation using the above general equation or its refined version. Insuch case, the control system is programmed with either equation, butwith the equation rearranged to solve for P2. The engine controllerprocesses certain data that is relevant to calculating desired enginefueling in terms of quantity of fuel injected per injection, or strokeof a fuel injector. The calculated data representing desired enginefueling is compared to a predefined limit that is contained in thecontrol system. The control system selects a predetermined constant asdata for P1 when the desired fueling data exceeds the predefined limit,but equates P1 to P2 by substituting P2 for P1 in the formula when thedesired fueling data is equal to or less than the predefined limit. Theresult of the processing is data that defines a value for P2, that inconjunction with the data for P1, defines the duration of a fuelinjection that will cause the quantity of fuel injected during theinjection at the prevailing injector control pressure ICP to besubstantially equal to the desired fueling, ignoring for the momentpossible adjustment due to factors that may call for some adjustment, asmentioned earlier, to compensate for certain influences. Even whenadjustment is made, the actual quantity injected is determined at leastin substantial part by the general formula, or its refined version, asrearranged to develop data for setting the duration of injectoractuation to produce one injection of fuel.

[0059] The present invention tailors the general formula, or its refinedversion, to take into account the particular calibration of each fuelinjector in an engine. FIG. 7 shows the injection characteristic foreach of several fuel injectors of the same type for an injector controlpressure of 6 Mpa. As can be seen, the characteristic is subject toinjector-to-injector variation, due essentially to slight variations inmanufacture employing mass production techniques.

[0060]FIG. 8 shows how the variable P2 must change for each fuelinjector in order for all fuel injectors to deliver the same quantity offuel per injection for a given desired fueling vfdes.

[0061] In accordance with the inventive method, each fuel injector isoperated at the conclusion of its manufacture, and certain measurementsare made. A specific example comprises operating a fuel injector at acertain higher injector control pressure and at a certain lower injectorcontrol pressure with the same electric actuating signal and measuringthe quantity of fuel injected in each instance. The two measurementswould described a straight line on a graph plot of quantity of injectedfuel vs. injector control pressure. This straight line is then comparedwith a straight line calculated by using the general formula.Substantial coincidence of the two lines would not call for anyadjustment of the general formula for this particular fuel injector whenthe fuel injector is operating in an engine. Lack of substantialcoincidence would call for an appropriate adjustment.

[0062] An appropriate adjustment is made by making certain changes incertain coefficients of the general formula that will result in valuesof P2 that when applied to this particular fuel injector, will secureits proper calibration in the engine. In order for the associated enginecontrol system to provide those coefficient changes, the fuel injectoris marked in a certain manner to identify how the coefficients should bemodified. Marking is preferably done electronically in a way that allowsthe engine control system to electronically read the marked data andcause the modified coefficients to be used in the general formulawhenever data for P2 is calculated for this particular fuel injector.

[0063] The engine control system has the capability to do this for eachfuel injector. FIGS. 9, 10, and 11 show examples of how the modificationof formula coefficients can secure calibration of three respective fuelinjectors in an engine.

[0064] It is possible that a particular control strategy may still attimes adjust the tailored formula to compensate for certain influencesthat call for compensation, such as cold starting for example.

[0065] Certain fuel injection strategies employ a pilot injection,followed by a main injection. Principles of the invention may be appliedto either or both types of injection in such an injection strategy.

[0066] While a presently preferred embodiment of the invention has beenillustrated and described, it should be appreciated that principles ofthe invention apply to all embodiments falling within the scope of thefollowing claims.

What is claimed is:
 1. A method of calibrating an electric-actuated fuel injector for an engine that uses injector control pressure to inject the fuel from the injector into the engine, before the fuel injector is installed in the engine, the method comprising: electrically actuating the fuel injector with a predetermined electric actuation at a first predetermined injector control pressure and measuring the resulting quantity of fuel injected; electrically actuating the fuel injector with the predetermined electric actuation at a second predetermined injector control pressure and measuring the resulting quantity of fuel injected; and correlating the measured quantities, the predetermined injection control pressures, and the applied predetermined electric actuation with values of quantity of fuel injected, injector control pressure, and electric actuation that are related by a predetermined multiple term mathematical formula to ascertain, for the same quantities of injected fuel at each predetermined injector control pressure, difference between the applied predetermined electric actuation and that required by the formula.
 2. A method as set forth in claim 1 further including marking the fuel injector with data that defines the difference.
 3. A method as set forth in claim 2 further including installing the fuel injector in an engine having a control system that contains the formula and includes one or more processors for processing the formula to calculate electric actuation of the fuel injector and modifying the formula according to the data marked on the fuel injector to calibrate the fuel injector in the engine so that the fuel injector injects fuel substantially in accordance with desired fueling data calculated by the control system and then used in the formula as the quantity of injected fuel.
 4. A method as set forth in claim 3 wherein the control system calibrates the fuel injector in the engine by modifying certain coefficients of the formula.
 5. A system for calibrating an electric-actuated fuel injector for an engine that uses injector control pressure to inject the fuel from the injector into the engine, before the fuel injector is installed in the engine, the system comprising: apparatus for 1) electrically actuating the fuel injector with a predetermined electric actuation at a first predetermined injector control pressure and measuring the resulting quantity of fuel injected; 2) electrically actuating the fuel injector with the predetermined electric actuation at a second predetermined injector control pressure and measuring the resulting quantity of fuel injected; and 3) correlating the measured quantities, the predetermined injection control pressures, and the applied predetermined electric actuation with values of quantity of fuel injected, injector control pressure, and electric actuation that are related by a predetermined multiple term mathematical formula to ascertain, for the same quantities of injected fuel at each predetermined injector control pressure, difference between the applied predetermined electric actuation and that required by the formula.
 6. A system as set forth in claim 5 including marking apparatus for marking the fuel injector with data that defines the difference.
 7. An internal combustion engine comprising: one or more electric-actuated fuel injectors each of which injects fuel into a respective combustion chamber of the engine as a function of injector control pressure and the duration of an electric actuating signal that sets the duration of a fuel injection to achieve an injection quantity determined at least in part by a desired fueling data representing desired fueling of the engine; and an engine control system comprising one or more processors that calculate the desired fueling data, and from the desired fueling data, the duration of the electric actuating signal for each fuel injector by processing the desired fueling data and data representing injector control pressure, including processing, according to a mathematical formula, data correlated with the desired fueling data and data representing injector control pressure, to develop data that the control system further processes to calculate the duration of the electric actuating signal; wherein each fuel injector is marked with data that is entered into the engine control system incidental to installation of the fuel injector in the engine and that defines difference between the operating characteristic of the fuel injector and that of a general fuel injector on which the multiple term mathematical formula is based, and the control system modifies the formula for each fuel injector according to the marked data on each fuel injector to thereby calibrate each fuel injector in the engine so that each fuel injector injects fuel substantially in accordance with desired fueling data that is calculated by the control system and then is used in the formula as the quantity of injected fuel.
 8. An internal combustion engine as set forth in claim 7 wherein the control system calibrates each fuel injector in the engine by modifying certain coefficients of the formula for each fuel injector. 